Methods and associated systems for simulating illumination patterns

ABSTRACT

Systems and methods for simulating illumination patterns on target surfaces in a space are disclosed. The system includes an input component and a simulation component. The input component receives a sampling angular range, a sampling polygon density, and a sampling polygon type. The simulation component traces sampling rays according to the sampling angular range and the sampling polygon density and type within a sampling range. The simulation component can further (1) generate an initial illumination pattern with a plurality of sampling polygon projections on the target surface; (2) assign the same value of an attribute in the sampling polygon projections defined by sampling rays through substantially the same route from the light source to the target surface; and (3) adjust the value of the attribute in the sampling polygon projection defined by sampling rays from different routes by interpolation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. ProvisionalApplication No. 81/642,015, filed May 3, 2012, and incorporated hereinby reference in its entirety.

TECHNICAL FIELD

The present technology relates generally to methods and systems forsimulating illumination patterns in optical design systems.

BACKGROUND

Conventional illumination design systems typically require significantcomputing resources and time to properly compute lighting patterns ontarget surfaces or regions. FIG. 1, for example, is a screen shot of auser interface 10 illustrating a conventional technique for simulatingillumination patterns. This technique includes projecting sampling raysfrom a light source point 101 toward a target surface 102. The samplingrays can be refracted, reflected, scattered, or diffracted by objects103, 104, 105, and 108. As shown in FIG. 1, for example, the object 103is a lens with an array of hexagons, the object 104 is a spheroid, theobject 105 is a cylinder, and the object 106 is a cuboid. In order tosimulate an illumination pattern of the light source 101 on the targetsurface 102, conventional simulation techniques typically requiretracing a large number of sampling rays (e.g., five million samplingrays) to get an idea of the light pattern on the target surface 102.Such techniques can be inefficient, costly, and require significantcomputing resources and processing time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a screen shot of a user interface illustrating a conventionaltechnique for simulating illumination patterns.

FIG. 2A is a schematic diagram of a sampling angle and sampling polygonsconfigured in accordance with an embodiment of the present technology.

FIG. 2B is a schematic diagram showing a sampling range in accordancewith an embodiment of the present technology.

FIG. 2C is a schematic diagram illustrating an interpolation techniqueconfigured in accordance with an embodiment of the present technology.

FIGS. 2D and 2E are schematic diagrams illustrating techniques forgenerating additional sampling polygons in accordance with embodimentsof the present technology.

FIGS. 3-5 are screen shots illustrating simulation results in accordancewith embodiments of present technology.

FIG. 6 is a flowchart illustrating various stages of a method or processfor simulating an illumination pattern on a target surface in accordancewith an embodiment of the present technology.

FIG. 7 is a flowchart illustrating various stages of another method orprocess for simulating an illumination pattern on a target surface inaccordance with another embodiment of the present technology.

A portion of this disclosure contains material to which a claim forcopyright is made. The copyright owner has no objection to the facsimilereproduction by anyone of the patent document or patent disclosure(including the Figures) as it appears in the U.S. Patent and TrademarkOffice patent file or records, but the copyright owner reserves allother copyright rights whatsoever.

DETAILED DESCRIPTION

The following disclosure is directed to methods and associated systemsfor simulating illumination patterns in optical design systems. Asdescribed in greater detail below, a method for simulating anillumination pattern on a target surface in a space in accordance withan embodiment of the present technology can include selecting a lightsource in the space, determining a sampling angle, a sampling range, anda sampling polygon type, and simulating a plurality of sampling raysaccording to the sampling angle and the sampling polygon type within thesampling range. This technique creates an initial illumination patternwith a plurality of sampling polygon projections on the target surface.The method also includes assigning the same value of an attribute in thesampling polygon projections defined by sampling rays throughsubstantially the same route from the light source to the targetsurface, and adjusting the value of the attribute in the samplingpolygon projection defined by sampling rays from different routes byinterpolation according to a predetermined detail requirement so as tofinalize the illumination pattern. The method further includesdisplaying the illumination pattern on a user interface.

One feature of the present technology is that instead of tracing a hugenumber of individual sampling rays, the disclosed interpolation schemescan be used to accurately and quickly estimate and model a selectednumber of sampling rays traveling to the target surface. Moreparticularly, a light source typically emits sampling rays through anentire selected angular range. The traveling paths of neighboringsampling rays are usually very similar (i.e., neighboring sampling rayshit the same objects in the space and in the same order, and reachapproximately the same position on the target surface, only withslightly different coordinates or reflective/refractive angles).Therefore, in contrast with conventional techniques that includesimulating or tracing very large numbers (e.g., millions) of samplingrays, the present technology utilizes interpolation schemes to estimatehow a small number of sampling rays travel to the target surface area,and using such data to approximate the appearance of lit scenes inoptical design programs/systems. These techniques are expected tosignificantly reduce the required processing time without sacrificingthe quality and/or accuracy of simulation results.

Certain details are set forth in the following description and in FIGS.2A-7 to provide a thorough understanding of various embodiments of thedisclosure. However, other details describing well-known structures andsystems often associated with visual displays and related opticalequipment and/or other aspects of visual display calibration systems arenot set forth below to avoid unnecessarily obscuring the description ofvarious embodiments of the disclosure.

Many of the details, dimensions, angles, and other features shown in theFigures are merely illustrative of particular embodiments of thedisclosure. Accordingly, other embodiments can have other details,dimensions, angles, and features without departing from the spirit orscope of the present disclosure. In addition, those of ordinary skill inthe art will appreciate that further embodiments of the disclosure canbe practiced without several of the details described below.

A. Embodiments of Methods and Systems for Simulating IlluminationPatterns

FIG. 2A is a schematic diagram of a sampling angle and sampling polygonsconfigured in accordance with an embodiment of the present technology.In the illustrated embodiment, sampling rays 210 emanate from a lightsource point 201 (i.e., vertex A) toward a target surface 202. Asdescribed in greater detail below, a user can effectively simulate ormodel an illumination pattern on the target surface 202 using thedisclosed technology in a fraction of the time it would take usingconventional techniques. In this embodiment, for example, a user canfirst determine a sampling angle θ. As shown in FIG. 2A, the samplingangle θ can be defined by two sampling rays (e.g., AB and AC). Smallersampling angles θ, for example, can result in more detailed simulationresults. Second, a user can select an appropriate sampling polygon type.In other embodiments, the target surface 102 can include more than onesurface. For example, the target surface 102 can include a first surfaceand a second surface substantially perpendicular to the second surface(e.g. two adjacent surfaces at a corner of a room).

In the embodiment shown in FIG. 2A, for example, the sampling polygonwith a triangular cross section (i.e., three sampling rays constitutethis kind of polygon; referred as “N=3” type). In other embodiments,however, the sampling polygon can be defined by any number of samplingrays. In the illustrated embodiment, three sampling polygons are shown:polygons ABCD, ACDE, and ADEF. These polygons are 3-sided polygons (plusone bottom surface, for four surfaces in total). In accordance with anembodiment of the present technology, if the sampling rays that definethe polygon have substantially the same traveling path, then the polygoncan represent a uniform value of an attribute, such as radiant energy,ray position, ray angle, transmission, or color of the ray. Based onthis concept, simulation of illumination patterns in accordance with thepresent technology uses a relatively small number of sampling rays tocreate an illumination pattern without significantly sacrificingaccuracy and/or quality. In polygon ABCD, for example, the constituentsampling rays (i.e., AB, AC, AD) ail have substantially the sametraveling path, so ail rays within the polygon ABCD can be considered ashaving the same value of an attribute (i.e., uniform). Thus, these threesampling rays (i.e., AB, AC, and AD) can be representative to all rayswithin the polygon ABCD. In this embodiment, polygons ACDE and ADEF havethe same configuration. In other embodiments, however, polygons ACDE andADEF may have a different arrangement.

In the embodiment shown in FIG. 2A, five sampling rays (i.e., AB, AC,AD, AE, AF) are simulated to create the illumination pattern of thetarget area (i.e., area BCEF, including three triangles BCD, CDE, andDEF) on the target surface 202. In some embodiments, one simulation fora vertex (e.g., vertices C, D, and E) is sufficient. In otherembodiments, however, a different number of sampling rays may be used.As noted above, one feature of the present technology is that thedisclosed techniques are expected to significantly reduce the computingburden of sampling ray simulation.

FIG. 2B is a schematic diagram showing a sampling range in accordancewith another embodiment of the present technology. The light sourcepoint 201 can emanate sampling rays 210 outwardly through a selectedangular range (e.g., three dimensions; 360°×360°) by any predeterminedsampling angle θ. In the illustrated embodiment, for example, thesampling range can be a hemisphere. In some embodiments, the samplingrange can be subdivided into a plurality of polygons, and then theillumination pattern on a target surface can be generated accordingly.For example, as shown in FIG. 2B, in some embodiments the sampling rangecan be a sphere 220 with an initial set of polygons. In otherembodiments, however, the sampling range may have a differentarrangement.

FIG. 2C is a schematic diagram illustrating an interpolation techniqueor process in accordance with an embodiment of the present technology.For embodiments in which the sampling rays constituting a polygon do nothave substantially similar traveling paths, further interpolation may beused to simulate the illumination pattern more accurately. For example,as shown in FIG. 2C, sampling rays (AB, AC, AD) constituting the polygonABCD all have a substantially similar traveling path and, accordingly,there is no need for further interpolation (i.e., a value of anattribute in this polygon is uniform or generally uniform). In contrast,the sampling rays (AE, AC, AD) constituting polygon AECD do not all havea substantially similar traveling path. For example, the sampling ray AEhits an object 203, and its traveling path is then reflected as OA′after the hitting vertex O. Thus, the polygon AECD can be interpolatedfurther.

In one embodiment, for example, the polygon AECD can be interpolatedusing a bisecting scheme. As shown in FIG. 2C, three additional verticesC′, D′, and E′ can be created at the middle of the lines CD, DE, and CE,respectively. Three additional sampling rays (i.e., AC′, AD′ and AE′)can be traced from the light source point 201, and four additionalsampling polygons can be generated: AEE′D′, AC′D′E′, ACC′E′, and AC′DD′.In this way, the accuracy of the simulation results may be enhanced byhaving more detailed sampling polygons.

The bisecting scheme described above is not the only method to generatemore detailed polygons from the light source point 201. Figures 2D and2E, for example, are schematic diagrams illustrating techniques forgenerating additional sampling polygons in accordance with furtherembodiments of the present technology. Referring first to FIG. 2D, newvertices B′, C and D′ can be added at any position of the lines BC, CDand BD, respectively, of the original polygon ABCD. More detailedsampling polygons can then be generated as part of the calculationprocess as discussed above.

Referring next to FIG. 2E, the original polygon ABCED may be defined byfour sampling rays (AB, AC, AD, and AE; referred as “N=4” type).Additional vertices B′, C, D′ E′ and, F can be added in the originalpolygon ABCDE, and additional five sampling rays (AB′, AC′, AD′, AE′ andAF) can be traced. Additional vertices B′, C′, D′ and E′ can be added atany position of the lines BC, CD, DE, and BE, respectively. Inadditional embodiments, further additional sampling polygons having avariety of suitable arrangements may be used.

FIGS. 3-5 are screen shots illustrating simulation results in accordancewith embodiments of the present technology. More specifically, FIGS. 3-5illustrate user interfaces 30, 40 and 50, respectively, includingdifferent simulation results of an illumination pattern on the targetsurface 102 from the light source point 101 (see FIG. 1; with the sameobjects 103, 104, 105, and 106) using simulation methods and process inaccordance with the present technology. In these embodiments, thesampling polygon type is a triangle (“N=3” type; defined by 3 samplingrays). The hexagonal shapes shown in FIGS. 3-5 are caused by an object(e.g., a lens with an array of hexagons). The user interface 30 in FIG.3 shows a “coarse” sampling, the user interface 40 in FIG. 4 shows a“medium” sampling, and the user interface 50 in FIG. 5 shows a “fine”sampling. The users can adjust the sampling level by choosing howdetailed their sampling polygons would be (see, for example, the FIGS.2C-2E and the corresponding description above).

In various embodiments, the “medium” sampling can have a samplingpolygon number twice than the sampling polygon number used in the“coarse” sampling. For example, the “coarse sampling” can create 500sampling polygons on a target surface, and then the “medium” samplingcan create 1000 sampling polygons on the target surface. Similarly, invarious embodiments, the “fine” sampling can have a sampling polygonnumber twice than the sampling polygon number used in the “medium”sampling. For example, the “medium sampling” can create 1000 samplingpolygons on a target surface, and then the “fine” sampling can create2000 sampling polygons on the target surface. In other embodiments, the“coarse,” “medium,” and/or “fine” sampling may include differentsampling numbers and/or different ratios relative to each other.

In certain embodiments, for example, the user can choose to skip thesubdivision simulation (e.g., the bisecting scheme discussed above) fora “coarse” sampling, such as shown in FIG. 3. In other embodiments, theuser can choose to conduct the subdivision simulation once for a“medium” sampling, such as shown in FIG. 4. In still furtherembodiments, the user can choose to do the subdivision simulation twicefor a “fine” sampling, as shown in FIG. 5. In some embodiments, a usercan determine how many times of subdivision simulation can be conduced.In other embodiments, the user can determine to repeat the subdivisionsimulation cycle until certain predetermined criterion has been met.

In certain embodiments, the user can opt to directly run the “fine” or“medium” sampling simulation in a specific direction. For example,certain types of anisotropic (e.g., directional) light sources, such asflashlights, projection lamps, or certain Light-Emitting Diode (LED)products, can have different light strength per unit area (such as,luminance, cd/m²) along different directions. For these types ofdirectional light sources, it can significantly reduce the simulation orprocessing time by focusing the simulation on a specific lightdirection. In certain embodiments, to improve simulation efficiency, theuser can conduct a pre-sampling simulation in certain directions incases where directional light sources are involved.

In other embodiments, more than one light source can be selected andsimulated. In still further embodiments, the light source is not limitedto point light sources. Line light sources, plane light sources, and/or3-dimension light sources can also be selected and simulated inaccordance with the present technology.

FIG. 6 is a flowchart illustrating various stages of a method or process600 for simulating an illumination pattern on a target surface inaccordance with an embodiment of the present technology. At stage 601,the method 600 includes selecting a light source (such as the lightsource point 201) to be simulated, and determining a sampling angle(e.g., sampling angle θ in FIGS. 2A-2E), a sampling range (e.g., ahemisphere), and a sampling polygon type (e.g., N=3 type, N=4 type, orN=6 type, as mentioned above).

At stage 602, the method 600 includes simulating the sampling raysaccording to the determined sampling angle, range, and polygon type, soas to create an initial illumination pattern with a plurality ofsampling polygon projections on the target surface.

At stage 603, the method 600 includes assigning the same value of anattribute (e.g., radiant energy, ray position, ray angle, transmission,or color of the ray) in the sampling polygon projections (e.g., the areaBCD on the target surface 202 in FIG. 2C) defined by sampling raysthrough substantially the same route (e.g., the polygon ABCD describedin FIG. 2C) from the light source to the target surface.

At stage 604, the method 600 includes adjusting the value of theattribute in the sampling polygon projection (e.g., the area CDE on thetarget surface 202 in FIG. 2C) defined by sampling rays from differentroutes (e.g., the polygon ACDE described in FIG. 2C) by interpolation(e.g., by methods described in FIG. 2D or 2E) according to apredetermined detail requirement (e.g., FIGS. 3-5) so as to finalize theillumination pattern.

At stage 605, the method 600 includes displaying the illuminationpattern on a user interface (e.g., the user interfaces 30, 40, and 50).In other embodiments, the method 600 can include different steps or thesteps can include a different arrangement. The method 600 can beperformed by any suitable computing systems under different type ofoperating systems, such as Microsoft Windows or Mac OS.

FIG. 7 is a flowchart illustrating various stages of another method orprocess 700 for simulating an illumination pattern on a target surfacein accordance with another embodiment of the present technology. Atstage 701, the method 700 includes selecting a light source (such as thelight source point 201) to be simulated, and determining a samplingangular range (e.g., θ in FIGS. 2A-2E), an initial sampling polygondensity (e.g., the number of expected polygon sampling projections onthe target surface; the actual sampling polygon density is subject tochange based on further interpolation as discussed below), and asampling polygon type (e.g., N=3 type, N=4 type, or N=6 type, asmentioned above) to define an initial polygon mesh (e.g., a set ofinitial polygon “frames” projected on the target surface, such as thepattern shown on the target surface 202 in FIG. 2C).

At stage 702, the method 700 includes tracing the sampling rays at eachpolygon vertex according to the determined sampling angular range,initial polygon density, and polygon type, and creating an initialillumination pattern with a plurality of sampling polygon projections onthe target surface.

At stage 703, the method 700 includes assigning luminous flux,triluminous flux, optical power, color, polarization, or otherattributes of the source to each of the rays in the polygon mesh. Atstage 704, the method 700 continues by determining if each set of raysassociated with a single polygon took substantially the same route fromthe light source to the target surface.

If the rays did not ail take the substantially the same route, at stage705 the method 700 includes subdividing the polygon into a number ofproportionally smaller polygons, and tracing new sampling rays at thevertices of the newly created polygons. In certain embodiments, stage705 may be repeated until any desired accuracy is achieved. In otherembodiments, the accuracy may be defined either by the number ofsubdivision cycles or by certain predetermined criterion, such asimportance of an attribute in the polygon being subdivided.

At stage 706, the method 700 includes applying the ray attribute datafrom each polygon to the desired target surface by interpolation betweenvertices to finalize the illumination pattern on the target surface. Themethod 700 continues at stage 707 with displaying the illuminationpattern on a user interface. In other embodiments, the method 700 caninclude different steps or the steps can include a differentarrangement. The method 700 can be performed by any suitable computingsystems under different type of operating systems, such as MicrosoftWindows or Mac OS. In certain embodiments, the method 700 can furtherinclude storing received and generated information in a storage device.Examples of the received information can include initial conditions,such as the received sampling angular range, the received initialsampling polygon density, and the received sampling polygon type. Anexample of the generated information is the generated illuminationpattern. In other embodiments, the method 700 can further includetransmitting the received and generated information via a network (e.g.,via the Internet).

The computing systems or devices on which the described technology maybe implemented may include one or more central processing units, memory,input devices (e.g., keyboard and pointing devices), output devices(e.g., display devices), storage devices (e.g., disk drives), andnetwork devices (e.g., network interfaces). The memory and storagedevices are computer-readable media that may store instructions thatimplement the system. In addition, the data structures and messagestructures may be stored or transmitted via a data transmission medium,such as a signal on a communications link. Various communications linksmay be used, such as the Internet, a local area network, a wide areanetwork, or a point-to-point dial-up connection.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense as opposed to anexclusive or exhaustive sense; that is to say, in the sense of“including, but not limited to.” Words using the singular or pluralnumber also include the plural or singular number respectively.Additionally, the words “herein,” “above,” “below” and words of similarimport, when used in this application, shall refer to this applicationas a whole and not to any particular portions of this application. Whenthe disclosure uses the word “or” in reference to a list of two or moreitems, that word covers all of the following interpretations of theword: any of the items in the list, ail of the items in the list and anycombination of the items in the list.

The detailed descriptions of embodiments of the technology are notintended to be exhaustive or to limit the invention to the precise formdisclosed above. While specific embodiments of, and examples for, thetechnology are described for illustrative purposes, various equivalentmodifications are possible within the scope of the technology, as thoseskilled in the relevant art will recognize. For example, while steps arepresented in a given order, alternative embodiments may perform routineshaving steps in a different order. Further, the elements and acts of thevarious embodiments described herein can be combined to provide furtherembodiments. Moreover, the teachings of the technology provided hereincan be applied to other systems, not necessarily the system describedherein.

These and other changes can be made to the technology in light of thedetailed description. In general, the terms used in the followingdisclosure should not be construed to limit the technology to thespecific embodiments disclosed in the specification, unless the abovedetailed description explicitly defines such terms. Accordingly, theactual scope of the technology encompasses the disclosed embodiments andail equivalent ways of practicing or implementing the technology.

1. A method for simulating an illumination pattern on a target surface in a space, the method comprising: selecting a light source in the space; determining a sampling angular range, an initial sampling polygon density, and a sampling polygon type; tracing a plurality of traveling paths according to the sampling angular range, the initial sampling polygon density, and sampling polygon type within the sampling angular range, so as to create an initial illumination pattern with a plurality of sampling polygon projections on the target surface; assigning a value of a light attribute to each of the sampling polygon projections; adjusting the value of the light attribute in at least one of the sampling polygon projections by interpolation in response to an event that one of the traveling path hits an object in the space so as to finalize the illumination pattern; and displaying the illumination pattern on a user interface.
 2. The method of claim 1, wherein the light source has a significant light strength per unit area in a predetermined direction, and wherein the method further comprises tracing a plurality of prior traveling paths in the predetermined direction before determining the sampling angular range, the initial sampling polygon density, and the sampling polygon type.
 3. The method of claim 1 wherein the sampling range comprises a hemisphere.
 4. (canceled)
 5. The method of claim 1 wherein the sampling polygon type comprises a 3-sided polygon, a 4-sided polygon, and/or a 6-sided polygon.
 6. (canceled)
 7. The method of claim 1 wherein the target surface comprises a first area with a first sampling polygon density and a second area with a second sampling polygon density, and wherein the first sampling polygon density is greater than the second sampling polygon density.
 8. A method for simulating an illumination pattern on a target surface in a space, the method comprising: selecting a light source in the space; determining a sampling angular range, an initial sampling polygon density, and a sampling polygon type to define a polygon mesh; tracing a plurality of traveling paths corresponding to vertices of the polygon mesh and creating an initial illumination pattern on the target surface, wherein the initial illumination pattern includes a plurality of sampling polygons projections; assigning a value of light attributes of the light source to each of the sampling polygon projections; determining sampling polygon projections to be subdivided in response to an event that one of the traveling paths hits an object in the space; selectively tracing additional traveling paths corresponding to the vertices of the sampling polygon projections to be subdivided; adjusting the value of the light attributes in at least one of the sampling polygon projections to be subdivided to finalize the illumination pattern on the target surface; and displaying the illumination pattern on a user interface.
 9. The method of claim 8, further comprising selecting a pre-sampling direction based on a light strength per unit area of the light source.
 10. The method of claim 8 wherein the polygon mesh comprises a first number of sampling polygons on the target surface during a coarse sampling, and wherein the polygon mesh comprises a second number of sampling polygons on the target surface during a medium sampling, and further wherein the second number is greater than the first number.
 11. The method of claim 9 wherein the polygon mesh comprises a third number of sampling polygons on the target surface during a fine sampling, and wherein the third number is greater than the second number.
 12. The method of claim 8 wherein the polygon mesh comprises a plurality of triangular projections on the target surface.
 13. The method of claim 8 wherein the light source further comprises a first light source and a second light source, and wherein the first light source has a greater light strength per unit area than the second light source.
 14. The method of claim 8 wherein the target surface further comprises a first surface and a second surface, and wherein the first surface is substantially perpendicular to the second surface.
 15. A system for simulating an illumination pattern from a light source on a target surface in a space, the system comprising: an input component configured to receive a sampling angular range, an initial sampling polygon density, and a sampling polygon type; and a simulation component configured to trace a plurality of traveling paths according to the sampling angular range, the initial sampling polygon density, and the sampling polygon type within the sampling angular range, wherein the simulation component is further configured to generate an initial illumination pattern with a plurality of sampling polygon projections on the target surface, wherein the simulation component is further configured to assign a value of a light attribute to each of the sampling polygon projections; and wherein the simulation component is further configured to adjust the value of the light attribute in the sampling polygon projections by interpolation in response to an event that one of the traveling path hits an object in the space to finalize the illumination pattern for display on a user interface.
 16. The system of claim 15 wherein the simulation component is further configured to: determine sampling polygons to be subdivided based upon determination of the traveling path; and selectively trace additional traveling paths corresponding to the vertices of the subdivided sampling polygons.
 17. The system of claim 15 wherein the light source has a significant light strength per unit area in a predetermined direction, and wherein the simulation component is configured to trace a plurality of prior traveling paths in the predetermined direction.
 18. The system of claim 15 wherein the sampling angular range comprises a hemisphere.
 19. The system of claim 15, further comprising: a first storage component configured to store the received sampling angular range, the received initial sampling polygon density, the received sampling polygon type and/or the illumination pattern; and a transmitting component configured to transmit the received sampling angular range, the received initial sampling polygon density, the received sampling polygon type and/or the illumination pattern to a second storage component through a network.
 20. The system of claim 15 wherein the initial illumination pattern is generated in accordance with the object in the space.
 21. The method of claim 1 wherein the target surface comprises a first surface and a second surface.
 22. The method of claim 1 wherein the interpolation comprises adding a new vertex between two existing vertices of the at least one of the sampling polygon projections. 